A small ball is held at the surface of liquid oil in a container. The ball is released from rest andfalls through the oil. The ball has velocity v. A viscous (drag) force F acts on the ball.Which graph could show the variation with v of F?
Question
A small ball is held at the surface of liquid oil in a container. The ball is released from rest andfalls through the oil. The ball has velocity v. A viscous (drag) force F acts on the ball.Which graph could show the variation with v of F?
Solution
The viscous (drag) force F acting on a ball moving through a fluid such as oil is often modeled as being proportional to the velocity v of the ball. This relationship is often written as F = kv, where k is a constant that depends on properties of the ball and the fluid.
Therefore, the graph of F versus v would be a straight line passing through the origin (0,0) with a positive slope. This is because when the velocity v is zero, the drag force F is also zero. As the velocity v increases, the drag force F also increases linearly.
So, the correct graph would be a straight line starting from the origin and going upwards to the right.
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